PRP Records

Probable Primes Top 10000

(294113 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 9001 10^99990-8111 99990 Patrick De Geest 02/2020 9002 2^332141-113073 99985 Enzo Doria 07/2014 9003 (1610172603037^8192+1610172602919^8192)/17110948127473666 99983 Youcef Lemsafer 01/2023 9004 6*10^99979-79 99980 Robert Price 03/2022 9006 (3^209561+2)/728101255 99978 Lelio R Paula 09/2013 9005 23827^15702+15702^23827 99978 Hans Havermann 04/2018 9007 2^332085+1865897 99968 Enzo Doria 03/2016 9008 (9787*2^332070-1)/936402369 99959 Lelio R Paula 05/2015 9009 2^332023+191 99949 Lelio R Paula 02/2011 9010 (6271^26321-1)/6270 99946 Serge Batalov 06/2022 9011 7*10^99944+27 99945 Robert Price 11/2020 9012 3188^28523-28523^3188 99931 Norbert Schneider 06/2023 9013 2^331938+71149 99924 Enzo Doria 04/2016 9014 2^331932-78795 99922 Lelio R Paula 09/2016 9015 2^331921+771 99919 Lelio R Paula 01/2013 9016 7947^25618-25618^7947 99916 Norbert Schneider 08/2023 9017 (3^209419-2)/5132755 99912 Lelio R Paula 09/2013 9018 2^331860-114989 99900 Enzo Doria 05/2015 9019 2^331746-11655 99866 Lelio R Paula 09/2016 9020 11^95891-28 99861 Lelio R Paula 08/2016 9021 (2^331694-5)/11 99849 Lelio R Paula 10/2013 9022 (3^209246+7)/64 99834 Lelio R Paula 09/2013 9023 25062^9617+9617^25062 99823 Hans Havermann 04/2018 9024 15^84866-52 99811 Lelio R Paula 08/2016 9025 13^89600+30 99810 Lelio R Paula 08/2016 9026 2^331527+100280245065 99800 Paul Bourdelais 10/2021 9027 22950^22309+22309^22950 99798 Hans Havermann 03/2018 9028 5^142772-38 99794 Lelio R Paula 08/2016 9029 (7482^25759-1)/7481 99787 Serge Batalov 06/2022 9030 (23*2^331459+1)/475 99778 Lelio R Paula 11/2013 9031 2^331416-331416+1 99767 Robert Price 10/2014 9032 2^331256-57 99718 Lelio R Paula 12/2012 9033 28192^3443+3443^28192 99714 Hans Havermann 03/2018 9034 2^331185+737 99697 Lelio R Paula 01/2013 9035 (4*10^99693+149)/9 99693 Robert Price 03/2017 9036 2^331154+1880527 99688 Enzo Doria 10/2016 9038 (19^77951+1)/20 99679 Paul Bourdelais 03/2010 9037 24354^12385+12385^24354 99679 Hans Havermann 03/2018 9039 2^331110+1870459 99675 Enzo Doria 05/2016 9040 5*2^331075+7 99665 Lelio R Paula 08/2014 9041 25776^7351+7351^25776 99659 Hans Havermann 02/2018 9042 (16*10^99656-31)/3 99657 Robert Price 03/2016 9043 (6059^26347-1)/6058 99652 Serge Batalov 06/2022 9044 (15544^23773-1)/15543 99642 Serge Batalov 06/2022 9046 2^330968+345 99632 Lelio R Paula 09/2016 9045 (2^330969+690)/2 99632 Stefano Morozzi 09/2020 9048 2*5^142528-7 99624 Lelio R Paula 11/2014 9047 2^330942+77329 99624 Enzo Doria 05/2016 9049 14^86914-99 99615 Lelio R Paula 08/2016 9050 (19*2^330902+1)/77 99611 Lelio R Paula 11/2013 9051 22971^21692+21692^22971 99610 Hans Havermann 03/2018 9052 2^330845+71687 99595 Enzo Doria 04/2016 9053 (26667^22501-1)/26666 99585 Serge Batalov 06/2022 9054 (23*2^330770+1)/3 99573 Lelio R Paula 11/2013 9055 24494^11613+11613^24494 99567 Hans Havermann 03/2018 9056 2^330735+8415 99562 Lelio R Paula 09/2016 9057 2^330720+74071 99557 Enzo Doria 04/2016 9058 (10405^24781-1)/10404 99548 Serge Batalov 06/2022 9060 31^66738-2 99531 Lelio R Paula 09/2013 9059 (9002^25171-1)/9001 99531 Serge Batalov 06/2022 9061 (5023^26893-1)/5022 99527 Serge Batalov 06/2022 9062 7*3^208567+4 99513 Lelio R Paula 08/2014 9063 (15881^23689-1)/15880 99511 Serge Batalov 06/2022 9064 (13*10^99508+47)/3 99509 Robert Price 01/2017 9065 2^330553+779 99507 Lelio R Paula 01/2013 9066 15^84606-94 99505 Lelio R Paula 08/2016 9067 (10^99497+173)/3 99497 Robert Price 05/2021 9068 9*10^99493-43 99494 Robert Price 09/2021 9069 6^127858+47 99493 Lelio R Paula 08/2016 9070 5^142337+48 99490 Lelio R Paula 08/2016 9071 7^117724-20 99489 Lelio R Paula 08/2016 9072 (559^36209-1)/558 99479 Serge Batalov 06/2022 9073 (13470^24091-1)/13469 99477 Serge Batalov 06/2022 9074 (29*10^99474-17)/3 99475 Erik Branger 09/2014 9075 (185*10^99466-11)/3 99468 Robert Price 10/2020 9076 (2^330410+2038)/2 99464 Stefano Morozzi 09/2020 9077 (9*2^330407-1)/7 99463 Lelio R Paula 03/2014 9078 (516*32^66077-175)/31 99458 Eric Chen 04/2023 9079 (2863^28771-1)/2862 99453 Serge Batalov 06/2022 9080 (2^330373+2114)/2 99452 Stefano Morozzi 09/2020 9081 (68*10^99441+7)/3 99443 Robert Price 03/2016 9082 10^99434+155571 99435 Patrick De Geest 04/2020 9083 10^99434-123456789 99434 Robert Price 02/2020 9084 10^99434-191237 99434 Patrick De Geest 04/2020 9085 46^59791-45^59791 99418 Jean-Louis Charton 01/2013 9086 23839^14802+14802^23839 99417 Hans Havermann 02/2018 9087 (2*10^99408+529)/9 99408 Robert Price 01/2017 9088 (2^330216+3510)/2 99405 Stefano Morozzi 09/2020 9089 53^57646-2 99398 Lelio R Paula 09/2013 9090 2^330165+1870025 99390 Enzo Doria 05/2016 9091 7*10^99383+97 99384 Robert Price 09/2021 9092 2^330142-155 99383 Lelio R Paula 12/2012 9093 2^330088-115259 99367 Enzo Doria 06/2015 9094 24216^12671+12671^24216 99354 Hans Havermann 01/2018 9095 Phi(200548,10)/3208769 99354 Makoto Kamada 04/2019 9096 (746*10^99303+1)/9 99305 Robert Price 02/2017 9097 3^208107+40 99293 Lelio R Paula 08/2016 9098 2^329843+211343 99293 Enzo Doria 08/2023 9099 (3939^27617-1)/3938 99291 Serge Batalov 06/2022 9100 (5*2^329833-1)/369 99288 Lelio R Paula 02/2014 9101 8*3^208093+5 99287 Lelio R Paula 08/2014 9102 5^142043+56 99284 Lelio R Paula 08/2016 9103 (13*10^99282-157)/9 99283 Robert Price 05/2021 9104 (10^99284+7)/53/67 99281 Alfred Reich 06/2021 9105 22*10^99275+7 99277 Robert Price 04/2016 9106 2^329778+1876189 99274 Enzo Doria 07/2016 9107 (149557^19321-1)/(149557^139-1) 99264 Ryan Propper 11/2023 9108 (6580^25997-1)/6579 99259 Serge Batalov 06/2022 9109 (2249^29611-1)/2248 99253 Serge Batalov 06/2022 9110 (10^99239-13)/3 99239 Robert Price 02/2017 9111 (1199^32233-1)/1198 99237 Serge Batalov 06/2022 9113 3^207987+62 99236 Lelio R Paula 08/2016 9112 (62*10^99235+91)/9 99236 Robert Price 07/2021 9114 2^329638+49 99231 Lelio R Paula 12/2012 9115 7^117413-18 99226 Lelio R Paula 08/2016 9116 2^329586-458903 99216 Enzo Doria 04/2015 9117 (6290^26119-1)/6289 99214 Serge Batalov 06/2022 9119 2^329553+101 99206 Lelio R Paula 12/2012 9118 (21297^22921-1)/21296 99206 Serge Batalov 06/2022 9120 2^329551-112897 99205 Enzo Doria 06/2014 9121 (3^207925+7)/50 99204 Lelio R Paula 09/2013 9122 6^127458-17993 99182 Enzo Doria 03/2013 9123 27197^4428+4428^27197 99166 Hans Havermann 10/2017 9124 (46*10^99143-1)/9 99144 Robert Price 12/2014 9125 (64*10^99135+161)/9 99136 Robert Price 08/2022 9126 7*10^99133+69 99134 Robert Price 10/2017 9127 (21701^22861-1)/21700 99132 Serge Batalov 06/2022 9128 18^78968-3065 99127 Enzo Doria 03/2013 9130 25927^6654+6654^25927 99122 Hans Havermann 10/2017 9129 87915!4+16 99122 Robert Price 09/2019 9131 2^329259+189 99117 Lelio R Paula 12/2012 9132 8*10^99113+39 99114 Robert Price 01/2017 9133 6^127364+77 99109 Lelio R Paula 08/2016 9134 (82*10^99103+143)/9 99104 Robert Price 06/2021 9135 (11414^24421-1)/11413 99083 Serge Batalov 06/2022 9136 (2^329135+1110)/2 99080 Stefano Morozzi 09/2020 9137 (22089^22807-1)/22088 99074 Serge Batalov 06/2022 9138 (59*10^99069+391)/9 99070 Robert Price 03/2021 9139 (797*10^99061-41)/9 99063 Robert Price 04/2022 9140 2^329058-287681 99057 Harrison Mesh 06/2022 9141 6^127285+13 99047 Lelio R Paula 08/2016 9142 (228581#+235862)/(2^3*11*71*151) 99044 Makoto Morimoto 10/2017 9143 2^329007+73283 99041 Enzo Doria 04/2016 9144 (145413^19321-1)/(145413^139-1) 99030 Ryan Propper 11/2023 9145 5*3^207543-8 99024 Lelio R Paula 08/2014 9146 (2^328930+570)/2 99018 Stefano Morozzi 09/2020 9147 2^328885+149 99005 Lelio R Paula 12/2012 9149 23392^17075+17075^23392 99004 Hans Havermann 09/2017 9148 (7424^25579-1)/7423 99004 Serge Batalov 06/2022 9150 (2^328879-9)/119 99001 Lelio R Paula 10/2013 9151 5^141618+54 98987 Lelio R Paula 08/2016 9152 2^328824+24391 98986 Enzo Doria 10/2023 9153 8*10^98982+51 98983 Robert Price 05/2017 9154 (21*2^328809-1)/7709 98979 Lelio R Paula 03/2014 9155 2^328794-2797601 98977 Enzo Doria 04/2016 9156 (88331^20011-1)/88330 98972 Serge Batalov 06/2022 9157 6^127176+5 98963 Lelio R Paula 11/2014 9158 2*10^98961-21 98962 Robert Price 09/2020 9159 24262^11989+11989^24262 98960 Hans Havermann 09/2017 9160 (60138^20707-1)/60137 98958 Serge Batalov 06/2022 9161 2^328700-109709 98949 Enzo Doria 04/2014 9162 (2^328698+1810)/2 98948 Stefano Morozzi 01/2021 9163 (1014^32917-1)/1013 98947 Serge Batalov 06/2022 9164 87771!4-128 98944 Robert Price 11/2019 9165 (4576^27031-1)/4575 98943 Serge Batalov 06/2022 9166 (2^328658+3042)/2 98936 Stefano Morozzi 09/2020 9167 (1933^30103-1)/1932 98923 Serge Batalov 06/2022 9168 46711!2-2^46711 98916 Robert Price 09/2015 9169 9*7^117037+4 98909 Lelio R Paula 11/2014 9170 127^47012+126 98905 Norbert Schneider 01/2019 9171 (93826^19891-1)/93825 98900 Serge Batalov 06/2022 9172 (2^328525+1250)/2 98896 Stefano Morozzi 09/2020 9173 (10^98890+149)/3 98890 Serge Batalov 12/2014 9174 22775^21978+21978^22775 98889 Hans Havermann 08/2017 9175 2^328497-216933 98888 Enzo Doria 05/2014 9176 2^328487+32769 98885 Lelio R Paula 08/2016 9177 3^207250-112358 98884 Enzo Doria 06/2014 9178 13^88754-90 98867 Lelio R Paula 08/2016 9179 2^328406+709 98861 Lelio R Paula 02/2013 9180 2*10^98860-21 98861 Robert Price 09/2020 9181 (17*2^328413-1)/16173 98860 Lelio R Paula 03/2014 9182 7^116976+76 98857 Lelio R Paula 08/2016 9183 (2^328378+2710)/2 98852 Stefano Morozzi 09/2020 9184 (25411^22441-1)/25410 98849 Serge Batalov 06/2022 9185 (18668^23143-1)/18667 98842 Serge Batalov 06/2022 9187 2^328335+1155 98839 Lelio R Paula 08/2016 9186 2^328333-349003 98839 Harrison Mesh 06/2022 9189 (3*2^328311+1)/5 98832 Lelio R Paula 11/2013 9188 287^40210+40210^287 98832 Norbert Schneider 11/2014 9190 (2^328284+9)/1325 98821 Lelio R Paula 10/2013 9191 (21*2^328258+1)/2125 98814 Lelio R Paula 11/2013 9192 (28623^22171-1)/28622 98806 Serge Batalov 06/2022 9193 24746^9825+9825^24746 98795 Hans Havermann 07/2020 9194 26620^5143+5143^26620 98793 Hans Havermann 07/2020 9195 65^54491+48 98788 Lelio R Paula 04/2016 9196 3^207042+98 98785 Lelio R Paula 08/2016 9197 (2^328121+3110)/2 98774 Stefano Morozzi 09/2020 9198 10^98754+73383 98755 Patrick De Geest 02/2021 9201 3^206977-112756 98754 Enzo Doria 07/2014 9200 10^98754-40000000001 98754 Robert Price 09/2020 9199 10^98754-169343 98754 Patrick De Geest 02/2021 9202 7^116846-50 98747 Lelio R Paula 08/2016 9203 (19152^23059-1)/19151 98740 Serge Batalov 06/2022 9204 23267^17512+17512^23267 98730 Hans Havermann 04/2020 9205 2^327967-28635 98728 Lelio R Paula 08/2016 9206 707^34642+34642^707 98710 Norbert Schneider 12/2017 9207 (10771^24481-1)/10770 98710 Serge Batalov 06/2022 9208 6^126850-47 98709 Lelio R Paula 08/2016 9209 (2^327886+2170)/2 98704 Stefano Morozzi 09/2020 9210 (22*10^98697+47)/3 98698 Robert Price 06/2021 9211 (139706^19321-1)/(139706^139-1) 98696 Ryan Propper 11/2023 9212 8*6^126830-7 98694 Lelio R Paula 11/2014 9213 11^94770-270 98693 Enzo Doria 08/2012 9214 (2^327846+3250)/2 98692 Stefano Morozzi 01/2021 9215 2^327832+43 98688 Lelio R Paula 12/2012 9216 2^327795+761 98677 Lelio R Paula 02/2013 9217 (2^327796+1522)/2 98677 Stefano Morozzi 09/2020 9218 10^98669+147411 98670 Patrick De Geest 11/2016 9220 10^98669-9^(98669-1) 98669 Robert Price 05/2016 9219 10^98669-105249 98669 Patrick De Geest 11/2016 9221 (7911^25309-1)/7910 98657 Serge Batalov 06/2022 9222 2^327671-109801 98639 Enzo Doria 04/2014 9223 24398^11037+11037^24398 98638 Hans Havermann 10/2019 9224 5^141090-14 98618 Lelio R Paula 08/2016 9225 20^75799+47 98617 Lelio R Paula 08/2016 9226 (5452^26393-1)/5451 98616 Serge Batalov 06/2022 9227 28101^3226+3226^28101 98597 Hans Havermann 07/2020 9228 2^327515-1017 98592 Lelio R Paula 08/2016 9229 6^126692+97681 98586 Mike Oakes 04/2011 9230 2^327467-741 98578 Lelio R Paula 08/2016 9231 (2947^28411-1)/2946 98566 Serge Batalov 06/2022 9232 22713^21800+21800^22713 98540 Hans Havermann 05/2020 9233 (2^327329+9)/19 98535 Lelio R Paula 10/2013 9234 7^116577-66 98519 Lelio R Paula 08/2016 9235 (3*2^327250+1)/7 98512 Lelio R Paula 11/2013 9236 23220^17479+17479^23220 98512 Hans Havermann 03/2020 9237 (2^327240+3798)/2 98509 Stefano Morozzi 02/2021 9238 (28514^22111-1)/28513 98502 Serge Batalov 06/2022 9239 (19*2^327192+1)/275 98494 Lelio R Paula 11/2013 9240 2^327162-66945 98486 Lelio R Paula 08/2016 9241 30139^1852+1852^30139 98484 Hans Havermann 02/2020 9242 23182^17703+17703^23182 98479 Hans Havermann 01/2020 9243 4*10^98472-3 98473 Erik Branger 11/2013 9244 26167^5794+5794^26167 98466 Hans Havermann 01/2020 9245 (6883*2^327047-1)/77 98453 Lelio R Paula 05/2015 9246 (71*10^98446+1)/9 98447 Serge Batalov 11/2010 9247 (2009^29803-1)/2008 98436 Serge Batalov 06/2022 9248 13^88363+94 98432 Lelio R Paula 08/2016 9249 48^58543-47^58543 98425 Jean-Louis Charton 11/2005 9250 6^126481+41 98422 Lelio R Paula 08/2016

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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